Data generation method and charged particle beam irradiation device

ABSTRACT

In one embodiment, a data generation method is for calculating a coverage of a polygon in each of a plurality of pixels obtained by dividing a target to be irradiated with a charged particle beam into predetermined sizes. The method includes dividing a parametric curve that defines a pattern shape into a plurality of parametric curves, calculating, for each of the plurality of parametric curves, an area of a region surrounded by a segment connecting end points among control points of the parametric curve and the parametric curve, calculating positions of vertexes of a figure having an area equivalent to the calculated area and having, as one side thereof, the segment connecting the end points, and generating the polygon by using the vertexes.

CROSS REFERENCE TO RELATED APPLICATION

This application is based upon and claims benefit of priority from theJapanese Patent Application No. 2020-159904, filed on Sep. 24, 2020, theentire contents of which are incorporated herein by reference.

FIELD

The present invention relates to a data generation method and a chargedparticle beam irradiation device.

BACKGROUND

As LSI circuits are increasing in density, the line width of circuits ofsemiconductor devices is becoming finer. To form a desired circuitpattern onto a semiconductor device, a method of reducing andtransferring, by using a reduction-projection exposure apparatus, onto awafer a highly precise original image pattern formed on a quartz isemployed. The highly precise original image pattern is written by usingan electron beam writing apparatus, in which a technology commonly knownas electron beam lithography is used.

A known example of the electron beam writing device is a multi-beamwriting device that achieves an improved throughput by radiating a lotof beams at one time by using multi-beams. In this multi-beam writingdevice, for example, an electron beam emitted from an electron gunpasses an aperture member having a plurality of openings. This formsmulti-beams, and blanking of each beam is controlled by a blankingplate. A beam that is not blocked is reduced by an optical system andreaches a desired position on a mask on which a pattern is to bewritten.

In electron beam writing using a multi-beam writing device, anirradiation amount of each beam is controlled by calculating a coverageof an input figure for each of pixels that are sections of apredetermined size obtained by division. Furthermore, also in a casewhere an irradiation amount is calculated by using sections (secondsections) larger than the pixels for deciding an irradiation amount ofeach beam, it is necessary to calculate a coverage in each of the secondsections. In a case where the input figure includes a curve, a coveragecan be calculated relatively easily by approximation to a polygon.However, high-precision approximation increases the number of vertexesof an approximate polygon, thereby undesirably taking a long time fordata processing.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a multi charged particle beam writingdevice according to an embodiment of the present invention.

FIG. 2 is a plan view of a shaping aperture array plate.

FIG. 3 is a flowchart for explaining a writing method.

FIG. 4 is a view for explaining writing operation.

FIG. 5 is a flowchart for explaining a pixel map generation method.

FIG. 6A illustrates an example of a B-spline curve, FIG. 6B illustratesan example of a Bezier curve, and FIG. 6C illustrates a conversionformula.

FIG. 7A illustrates an example of a Bezier curve, and FIG. 7Billustrates an example of division of the Bezier curve.

FIG. 8A illustrates an example of a Bezier curve, FIG. 8B illustrates anexample of division of the Bezier curve, and FIGS. 8C and 8D illustratean example of a Bezier curve obtained by the division.

FIG. 9 is a view for explaining an area of a curved portion of a Beziercurve.

FIG. 10 illustrates an example of a trapezoid having the same area asthe curve portion.

FIG. 11 illustrates an example of a triangle having the same area as thecurve portion.

FIG. 12 illustrates an example of a triangle having the same area as thecurve portion.

FIGS. 13A and 13B illustrate an example of generation of a polygon, andFIG. 13C illustrates superimposition of approximate polygons.

FIG. 14A illustrates an example of generation of a polygon, and FIG. 14Billustrates superimposition of approximate polygons.

FIGS. 15A and 15B illustrate generation of a polygon.

FIGS. 16A and 16B illustrate generation of a polygon.

DETAILED DESCRIPTION

In one embodiment, a data generation method is for calculating acoverage of a polygon in each of a plurality of pixels obtained bydividing a target to be irradiated with a charged particle beam intopredetermined sizes. The method includes dividing a parametric curvethat defines a pattern shape into a plurality of parametric curves,calculating, for each of the plurality of parametric curves, an area ofa region surrounded by a segment connecting end points among controlpoints of the parametric curve and the parametric curve, calculatingpositions of vertexes of a figure having an area equivalent to thecalculated area and having, as one side thereof, the segment connectingthe end points, and generating the polygon by using the vertexes.

An embodiment of the present invention will be described below withreference to the drawings. In the embodiment, a configuration using anelectron beam as an example of a charged particle beam will bedescribed. The charged particle beam is not limited to the electronbeam. For example, the charged particle beam may be an ion beam.

First Embodiment

FIG. 1 illustrates an outline configuration of a writing device 100according to the first embodiment. As illustrated in FIG. 1 , thewriting device 100 includes a writing unit 150 and a control unit 160.The writing device 100 is an example of a multi charged particle beamwriting device. The writing unit 150 includes an electron lens barrel102 and a writing chamber 103. In the electron lens barrel 102, anelectron gun 201, a lighting lens 202, a shaping aperture array plate203, a blanking aperture array plate 204, a reducing lens 205, alimiting aperture member 206, an objective lens 207, and a deflector 208are disposed.

In the writing chamber 103, an XY stage 105 is disposed. A substrate 101on which a pattern is to be written is disposed on the XY stage 105. Thesubstrate 101 is, for example, mask blanks or a semiconductor substrate(silicon wafer). Furthermore, a mirror 210 for position measurement isdisposed on the XY stage 105.

The control unit 160 has a control calculator 110, a deflection controlcircuit 130, a stage position detector 139, and a storage unit 140. Thestorage unit 140 stores therein writing data supplied from an outside.In the writing data, information on a plurality of figure patternsdescribing patterns to be formed on the substrate 101 is defined. Thefigure patterns include a curve, and a shape thereof is defined, forexample, by a cubic B-spline curve.

The control calculator 110 has an area density calculation unit 111, anirradiation time calculation unit 112, a data processing unit 113, and awriting control unit 114. Each unit of the control calculator 110 may berealized by hardware such as an electric circuit or may be realized bysoftware such as programs that execute these functions. Alternatively,each unit of the control calculator 110 may be realized by a combinationof hardware and software.

The stage position detector 139 irradiates the mirror 210 with a laser,receives reflected light, and detects a position of the XY stage 105 byusing the principle of laser interferometry.

FIG. 2 is a conceptual diagram illustrating a configuration of theshaping aperture array plate 203. As illustrated in FIG. 2 , the shapingaperture array plate 203 has a plurality of openings 203 a formed atpredetermined intervals along a lengthwise direction (y direction) and alateral direction (x direction). The openings 203 a are preferablyrectangles or circles having the same dimension and shape. A part of anelectron beam 200 passes each of the plurality of openings 203 a, andthus multi-beams 20 are formed.

The blanking aperture array plate 204 has passage holes at positionscorresponding to the openings 203 a of the shaping aperture array plate203. A blanker made up of a pair of electrodes is disposed in eachpassage hole. Of the two electrodes of the blanker, for example, oneelectrode is grounded and kept at a ground potential, and the otherelectrode is switched to a ground potential or a potential other thanthe ground potential. This switches OFF/ON of deflection of a beampassing a passage hole, thereby controlling blanking. In a case wherethe blanker does not deflect a beam, the beam is ON. In a case where theblanker deflects a beam, the beam is OFF. In this way, the plurality ofblankers perform blanking deflection of corresponding beams ofmulti-beams that have passed the plurality of openings 203 a of theshaping aperture array plate 203.

The electron beam 200 emitted from the electron gun 201 (emitting unit)illuminates the whole shaping aperture array plate 203 due to thelighting lens 202. The electron beam 200 illuminates a region includingall of the openings 203 a. The electron beam 200 passes the plurality ofopenings 203 a of the shaping aperture array plate 203, and thus aplurality of electron beams (multi beams) 20 having, for example, arectangular shape is formed.

The multi-beams 20 pass corresponding blankers of the blanking aperturearray plate 204. Each of the blankers performs blanking deflection of abeam that is switched off among electron beams that individually passthe blankers. Each of the blankers does not perform blanking deflectionof a beam that is switched on. The multi-beams 20 that have passed theblanking aperture array plate 204 are reduced by the reducing lens 205and travel toward a central opening of the limiting aperture member 206.

A beam that is controlled to a beam off state is deflected by theblanker and travels along a path passing an outside of the opening ofthe limiting aperture member 206 and is therefore blocked by thelimiting aperture member 206. Meanwhile, a beam that is controlled to abeam on state is not deflected by the blanker and therefore passes theopening of the limiting aperture member 206. In this way, blankingcontrol is performed by ON/OFF of deflection of the blanker, and thusON/OFF of a beam is controlled. The blanking aperture array plate 204functions as an irradiation time control unit that controls anirradiation time of each beam of multi-beams.

The limiting aperture member 206 allows beams deflected to a beam ONstate by the blankers of the blanking aperture array plate 204 to passtherethrough and blocks beams deflected to a beam OFF state by theblankers of the blanking aperture array plate 204. One shot ofmulti-beams is formed by beams formed from beam ON to beam OFF andhaving passed the limiting aperture member 206.

The multi-beams that have passed the limiting aperture member 206 arefocused by the objective lens 207 and form a pattern image of a desiredreduction rate on the substrate 101. The beams (whole multi-beams) thathave passed the limiting aperture member 206 are collectively deflectedby the deflector 208 in the same direction and reach a desired positionon the substrate 101.

In a case where the XY stage 105 is continuously moving, a beamirradiation position is controlled by the deflector 208 so as to followmovement of the XY stage 105 at least while the substrate 101 isirradiated with the beams. The multi-beams that are radiated one timeare ideally arranged at intervals obtained by multiplying the intervalsat which the plurality of openings 203 a of the shaping aperture arrayplate 203 are arranged by the desired reduction rate.

Next, a pattern writing method according to the present embodiment isdescribed with reference to the flowchart illustrated in FIG. 3 . In apattern area density calculation step (step S1), the area densitycalculation unit 111 virtually divides a writing region of the substrate101 into a plurality of mesh regions. A size of each of the mesh regionsis, for example, equivalent to a size of a single beam, and each of themesh regions becomes a pixel (unit irradiation region). The area densitycalculation unit 111 reads out writing data from the storage unit 140,calculates a pattern area density (coverage) p of each pixel by using apattern defined in the writing data, and generates a pixel map thatdefines a coverage of each pixel. A method for generating the pixel mapwill be described later.

In an irradiation time calculation step (step S2), the irradiation timecalculation unit 112 calculates an irradiation amount ρD₀ of a beam withwhich each pixel is irradiated by multiplying the pattern area density ρwith a reference irradiation amount D₀. The irradiation time calculationunit 112 may further multiply a correction coefficient for correcting aproximity effect or the like. The irradiation time calculation unit 112calculates an irradiation time of each of the plurality of beams thatconstitute the multi-beams by dividing the irradiation amount by acurrent amount of the beam.

In an irradiation time control data generation step (step S3), the dataprocessing unit 113 generates irradiation time control data byrearranging the irradiation time data in a shot order according to awriting sequence.

In a data transfer step (step S4), the writing control unit 114 suppliesthe irradiation time control data to the deflection control circuit 130.The deflection control circuit 130 supplies the irradiation time controldata to each blanker of the blanking aperture array plate 204.

In a writing step (step S5), the writing control unit 114 controls thewriting unit 150 to perform writing processing on the substrate 101.Each blanker of the blanking aperture array plate 204 gives a desiredexposure amount to each pixel by switching ON/OFF of a beam on the basisof the irradiation time control data.

FIG. 4 is a conceptual diagram for explaining writing operation. Asillustrated in FIG. 4 , the writing region 80 of the substrate 101 is,for example, virtually divided into a plurality of stripe regions 82having a strip shape of a predetermined width in a y direction (firstdirection). First, the XY stage 105 is moved so that an irradiationregion (beam array) 84 that can be irradiated by one irradiation ofmulti-beams is located at a left end of the first stripe region 82, andthen writing starts.

When the first stripe region 82 is written, writing is performed in a +xdirection relatively by moving the XY stage 105 in a −x direction. TheXY stage 105 is continuously moved at a predetermined speed. After endof the writing of the first stripe region 82, the stage position ismoved in the −y direction so that the beam array 84 is located at aright end of the second stripe region 82. Next, writing is performed inthe −x direction by moving the XY stage 105 in the +x direction.

In the third stripe region 82, writing is performed in the +x direction,and in the fourth stripe region 82, writing is performed in the −xdirection. A writing time can be shortened by performing writing whilealternately changing a direction. Alternatively, the stripe regions 82may be always written in the same direction, that is, either the +xdirection or the −x direction.

Next, a method for generating a pixel map by the area densitycalculation unit 111 is described with reference to the flowchartillustrated in FIG. 5 .

The area density calculation unit 111 reads out writing data from thestorage unit 140 and converts a curve of a figure pattern defined by acubic B-spline curve into a cubic (third-order) Bezier curve (stepS101). For example, the cubic B-spline curve illustrated in FIG. 6A isconverted into a cubic Bezier curve illustrated in FIG. 6B. FIG. 6Cillustrates an example of a conversion formula.

A cubic Bezier curve is expressed by four control points, as illustratedin FIG. 7A. That is, in the example illustrated in FIG. 6B, consecutivecombinations of four control points surround a figure. Among the fourcontrol points, two control points (end points), specifically, a startpoint and a termination point are located on a curve.

The area density calculation unit 111 divides a Bezier curve expressedby four control points into smaller Bezier curves at a position of aninflection point (step S102). The inflection point is a point at whichcurvature=(dPx/dt)(dPy²/dt²)−(dPy/dt)(dPx²/dt²)=0.

For example, a Bezier curve K0 illustrated in FIG. 7A includes a singleinflection point and is therefore divided into two Bezier curves K1 andK2 as illustrated in FIG. 7B. Bezier curves obtained after division atan inflection point do not cross straight lines connecting four controlpoints in order.

Next, an index for determining whether or not control points (directionpoints) are sufficiently proximal to a Bezier curve is calculated (stepS103). For example, assume that a Bezier curve K10 is defined by fourcontrol points C10, C11, C12, and C13, as illustrated in FIG. 8A.

The area density calculation unit 111 calculates a size of a boundingbox B1 that surrounds a quadrangle whose vertexes are the controlspoints C10, C11, C12, and C13 as an index indicative of a degree ofproximity of the control points to the Bezier curve. The size of thebounding box B1 may be an area of the bounding box B1 or may be a widthBLx and/or a height BLy of the bounding box B1.

In a case where the calculated index is larger than a predeterminedthreshold value (Yes in step S104), the area density calculation unit111 determines that the control points (the direction points C11 andC12) are away from the Bezier curve and redivides the Bezier curve intosmaller Bezier curves (step S105).

For example, as illustrated in FIG. 8B, the Bezier curve K10 (firstparametric curve) is redivided at an intermediate point (t=0.5) into aBezier curve K11 and a Bezier curve K12, and control points that definethe Bezier curves K11 and K12 (second parametric curves) are found.

The Bezier curve K11 is defined by control points C20, C21, C22, andC23. The Bezier curve K12 is defined by control points C23, C24, C25,and C26. The control points C20 and C26 are identical to the controlpoints C10 and C13 of FIG. 8A. The control point C23 is an intermediatepoint at which the Bezier curve K10 was redivided.

As illustrated in FIGS. 8C and 8D, the area density calculation unit 111calculates, for each of the Bezier curves K11 and K12, an index fordetermining whether or not the control points are sufficiently proximalto the Bezier curve (step S103). For example, the area densitycalculation unit 111 calculates a width BLx and/or a height BLy of abounding box B2 that surrounds a quadrangle whose vertexes are thecontrol points C20, C21, C22, and C23. Furthermore, the area densitycalculation unit 111 calculates a width BLx and/or a height BLy of abounding box B2 that surrounds a quadrangle whose vertexes are thecontrol points C23, C24, C25, and C26.

For all Bezier curves, redivision of the Bezier curve and calculation ofan index are repeated until the index becomes equal to or smaller than apredetermined threshold value (steps S103 to S105). In a case where awidth and/or a height are used as the index, it is desirable that avalue of the threshold value is about a size of a section for which acoverage is to be found.

When the index becomes equal to or smaller than the predeterminedthreshold value for all Bezier curves (No in step S104), the areadensity calculation unit 111 calculates an area Ac of a curve portion ofthe Bezier curve (step S106). In the case of a Bezier curve K defined bycontrol points C0, C1, C2, and C3 illustrated in FIG. 9 , the area Ac ofthe curve portion is an area of a region (the shaded portion in FIG. 9 )surrounded by a segment connecting the control point (end points) C0 andC3 and a Bezier curve between the control points C0 and C3 can becalculated by a formula of the Bezier curve and a line integral usingthe Green's theorem.

The area density calculation unit 111 generates a figure whose bottomside is the segment connecting the control points C0 and C3 and whosearea is equivalent to Ac calculated in step S106 (step S107). Thegenerated figure is a trapezoid or a triangle. A case where areas areequivalent encompasses not only a case where the areas are identical,but also a case where a difference (error) between the areas fallswithin a predetermined range. It is preferable to generate a figurewhose area is identical to Ac. In the embodiment below, a method forfinding a trapezoid or a triangle having the area Ac is described.

For example, as illustrated in FIG. 10 , a trapezoid whose bottom side(lower base) is the segment connecting the control points C0 and C3 isgenerated. The trapezoid has the control points C0 and C3 and vertexesV1 and V2 as vertexes thereof. The vertex V1 is located on a segmentconnecting the control point C0 and the control point C1. The vertex V2is located on a segment connecting the control point C2 and the controlpoint C3. The area density calculation unit 111 calculates coordinates(P1x, P1y) of the vertex V1 and coordinates (P2x, P2y) of the vertex V2assuming that coordinates of the control point C0 are an origin (0, 0).

The following formula 1 is established where h is a height of thistrapezoid, LB is a length of the lower base, α is an inclination of astraight line connecting the control point C0 and the control point C1,and β is an inclination of a straight line connecting the control pointC2 and the control point C3.a·h ² +b·h+c=0a=(1/β−1/α)×0.5b=2×LBc=Ac  (Formula 1)

The height h of the trapezoid is found from the above formula 1. Thecoordinates (P1x, P1y) of the vertex V1 and coordinates (P2x, P2y) ofthe vertex V2 are as follows.P1x=h/αP1y=hP2x=LB+h/βP2y=h

In this way, the trapezoid having the control points C0 and C3 and thevertexes V1 and V2 as vertexes thereof and having the area Ac isgenerated.

Furthermore, for example, as illustrated in FIG. 11 , a triangle whosebottom side is the segment connecting the control points C0 and C3 andhaving the area Ac is generated. This triangle has the control points C0and C3 and the vertex V3 as vertexes thereof. The vertex V3 is locatedon a bisector BS of an angle formed between a straight line connectingthe control point C0 and the control point C1 and a straight lineconnecting the control point C2 and the control point C3. Anintersection of the straight line connecting the control point C0 andthe control point C1 and the straight line connecting the control pointC2 and the control point C3 is referred to as M1. An intersection of thebisector BS and the bottom side of the triangle is referred to as M2.

Coordinates (P3x, P3y) of the vertex V3 are found from the followingformula 2 where h is a height of this triangle, LB is a length of thebottom side, La is a length from the control point C0 to theintersection M1, Lb is a length from the control point C3 to theintersection M1, la is a length from the control point C0 to theintersection M2, lb is a length from the control point C3 to theintersection M2, α is an inclination of the bisector BS, and (Mx, My) iscoordinates of the intersection M1.P3x=la+(h/α)P3y=h=2×Ac/LBla=La×LB/(La+Lb)α=My(Mx−la)  (Formula 2)

The triangle whose bottom side is the segment connecting the controlpoints C0 and C3 and having the area Ac may be a triangle whose vertexV4 is located on a perpendicular bisector Q of the segment connectingthe control points C0 and C3, as illustrated in FIG. 12 . In this case,coordinates (P4x, P4y) of the vertex V4 are found from the followingformula 3 by using the length LB of the bottom side.P4x=LB/2P4y=h=2×Ac/LB  (Formula 3)

Next, the area density calculation unit 111 generates a polygon bydrawing segments connecting the start point and end point (C0 and C3) ofeach Bezier curve and the vertexes found in step S107 in order (stepS108). For example, in the example of FIG. 10 , a polygon is generatedby connecting the points C0, V1, V2, and C3 in order. In the example ofFIG. 11 , a polygon is generated by connecting the points C0, V3, and C3in order. In the example of FIG. 12 , a polygon is generated byconnecting the points C0, V4, and C3 in order.

The area density calculation unit 111 divides the generated polygon intotriangles by a known method (step S109). The generated polygon need notbe divided into triangles and may be divided by using trapezoids.

The area density calculation unit 111 generates a pixel map bycalculating a coverage (area density) of a polygon in each pixel byusing triangles obtained by dividing the polygon (step S110). This pixelmap is used when the irradiation time calculation unit 112 calculates anirradiation amount of a beam with which each pixel is irradiated.

As described above, according to the present embodiment, a Bezier curveis divided to such a degree that an interval between vertexes does notbecome too small relative to a size of a section for which a coverage isto be found, a figure (a trapezoid or a triangle) having an areaequivalent to a curve portion of a Bezier curve obtained after thedivision is generated, and a polygon is generated by using vertexes ofthis figure. Since a high-precision approximate polygon that preservesan area in a region equivalent to a section size while suppressing thenumber of vertexes can be generated, a pixel coverage can be calculatedspeedily and accurately.

Second Embodiment

In electron beam writing, multiple writing, in which a necessaryirradiation amount is divided among plural writings (exposures), issometimes performed. In this case, vertexes used to generate a polygonfor calculation of an irradiation amount may differ from one writing(pass) to another.

First, a Bezier curve is divided so that an index becomes equal to orsmaller than a predetermined threshold value by performing steps S101 toS105 of FIG. 5 . For example, a Bezier curve K10 is redivided at anintermediate point into a Bezier curve K11 and a Bezier curve K12, asillustrated in FIGS. 8A and 8B. In a case where t=0 corresponds tocontrol points C10 and C20 and t=1 corresponds to control points C13 andC26, t=0.5 is the intermediate point. The Bezier curve K11 is defined bycontrol points C20, C21, C22, and C23. The Bezier curve K12 is definedby control points C23, C24, C25, and C26.

After the division of the Bezier curve, to calculate an irradiationamount in writing at a k-th pass (k is an integer of 1 or more), a k-thpixel map is generated by generating a polygon by drawing segmentsconnecting t=0 (the control point C20), t=0.5/k, t=0.5+0.5/k, and t=1(the control point C26) in order. An irradiation amount of a beam withwhich each pixel is to be irradiated is calculated by using the k-thpixel map.

For example, in writing at the first pass (k=1), a first pixel map isgenerated by generating a polygon by drawing segments connecting thecontrol points C20, C23, and C26, which are t=0, t=0.5, and t=1, inorder, as illustrated in FIG. 13A. An irradiation amount of a beam withwhich each pixel is to be irradiated in writing at the first pass iscalculated by using the first pixel map.

In writing at the second pass (k=2), a second pixel map is generated bygenerating a polygon by drawing segments connecting the control pointC20, which is t=0, a point V11, which is t=0.25, a point V12, which ist=0.75, and the control point C26, which is t=1, in order, asillustrated in FIG. 13B. An irradiation amount of a beam with which eachpixel is to be irradiated in writing at the second pass is calculated byusing the second pixel map.

In multiple writing whose number of passes is 2, a polygon illustratedin FIG. 13C is obtained by superimposing the polygon at the first passand the polygon at the second pass and has a shape approximate to theBezier curve.

In writing at the third pass (K=3), a third pixel map is generated bygenerating a polygon by drawing segments connecting the control pointC20, which is t=0, a point V13, which is t=0.17, a point V14, which ist=0.67, and the control point C26, which is t=1, in order, asillustrated in FIG. 14A. An irradiation amount of a beam with which eachpixel is to be irradiated in writing at the third pass is calculated byusing the third pixel map.

In multiple writing whose number of passes is 3, a polygon illustratedin FIG. 14B is obtained by superimposing the polygons at the first tothird passes and has a shape more approximate to the Bezier curve.

As described above, a polygon is generated by using points that (atleast partially) differ from one pass to another, and a pixel map isgenerated by using such a polygon. This can average errors ofapproximate polygons while keeping the number of vertexes small, therebyallowing speedy and accurate calculation of a pixel coverage.

A method for generating a polygon on an outer side of a Bezier curve bydrawing segments connecting all control points of the Bezier curve inorder and a method for generating a polygon on an inner side of theBezier curve by drawing segments connecting only end points amongcontrol points of the Bezier curve may be combined.

For example, in writing at the first pass, a pixel map is generated bygenerating a polygon on an outer side of the curve by drawing segmentsconnecting the control points C20 to C26 in order, as illustrated inFIG. 15A. An irradiation amount of a beam with which each pixel is to beirradiated in writing at the first pass is calculated by using thispixel map.

In writing at the second pass, a pixel map is generated by generating apolygon on an inner side of the curve by drawing segments connecting thecontrol points C20, C23, and C26 in order, as illustrated in FIG. 15B.An irradiation amount of a beam with which each pixel is to beirradiated in writing at the second pass is calculated by using thispixel map.

By superimposing the approximate polygon illustrated in FIG. 15A and theapproximate polygon illustrated in FIG. 15B, approximation errors areaveraged, and a pixel coverage can be calculated precisely.

Furthermore, a polygon may be generated by drawing segments connectingend points among control points of each Bezier curve and any one of twodirection points in order. A direction point used for generation of apolygon is changed for each pass of multiple writing.

For example, in writing at the first pass, a pixel map is generated bygenerating a polygon by drawing segments connecting the control pointsC20, C21, C23, C24, and C26 in order, as illustrated in FIG. 16A. Anirradiation amount of a beam with which each pixel is to be irradiatedin writing at the first pass is calculated by using this pixel map.

In writing at the second pass, a pixel map is generated by generating apolygon by drawing segments connecting the control points C20, C22, C23,C25, and C26 in order, as illustrated in FIG. 16B. An irradiation amountof a beam with which each pixel is to be irradiated in writing at thesecond pass is calculated by using this pixel map.

By superimposing the approximate polygon illustrated in FIG. 16A and theapproximate polygon illustrated in FIG. 16B, approximation errors areaveraged, and a pixel coverage can be calculated precisely.

Although a case where each polygon uses end points when polygons havingdifferent shapes for respective passes of multiple writing are generatedhas been described above, end points need not necessarily be used, andit is only necessary to generate polygons having different shapes byusing control points that differ from one pass to another.

Although an example in which a curve of a figure pattern defined by acubic B-spline curve is converted into a cubic Bezier curve has beendescribed in the first and second embodiments, an order of a parametriccurve is not limited to 3.

Although an example in which an input figure is expressed by a B-splinehas been described in the first and second embodiments, a figureexpressed by any of other parametric curves may be input data, as longas the figure can be converted into a Bezier curve.

The above processing may be performed by using a parametric curve otherthan a Bezier curve. The parametric curve is divided until an indexbecomes equal to or lower than a predetermined threshold value. Afterthe division, vertexes of a figure (a trapezoid or a triangle) having anarea equivalent to a curve portion of the parametric curve are found,and a polygon is generated by using the found vertexes. Alternatively,polygons are generated by using points that differ from one pass ofmultiple writing to another.

Although an example in which a figure (a trapezoid or a triangle) havingan area equivalent to a curve portion of a parametric curve obtainedafter division is generated has been described in the above embodiments,a dose amount may be set equivalent to the original curve portion bycombining an area of the generated figure and a dose modulation rate ofthe figure. For example, in a case where the area of the curve portionis 1.0, a figure having an area of 0.8 may be generated and a dosemodulation rate of this figure may be set to 1.25.

Although a writing device that writes a pattern on a substrate has beendescribed in the above embodiments, the present invention is alsoapplicable to other irradiation devices such as an inspection devicethat irradiate a target object with a beam. Although a multi-beamirradiation device that radiate a lot of beams at one time by usingmulti-beams has been described in the above embodiments, a similarmethod is also applicable to a single-beam irradiation device thatirradiates a target substrate with a single beam.

At least part of the control calculator 110 described in the aboveembodiments may be implemented in either hardware or software. Whenimplemented in software, a program that realizes at least part offunctions of the control calculator 110 may be stored on a recordingmedium such as a flexible disk or CD-ROM and read and executed by acomputer. The recording medium is not limited to a removable recordingmedium such as a magnetic disk or optical disk, but may be anon-removable recording medium such as a hard disk device or memory.

The program that realizes at least part of the functions of the controlcalculator 110 may be distributed through a communication line(including wireless communications) such as the Internet. Further, theprogram may be encrypted, modulated, or compressed to be distributedthrough a wired line or wireless line such as the Internet or to bedistributed by storing the program on a recording medium.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. For example, although the above embodimentsemploy the variable formation beam that is shaped at each shot and isirradiated, a beam having a definite shape may be irradiated. Aplurality of beams can be irradiated simultaneously. Indeed, the novelmethods and systems described herein may be embodied in a variety ofother forms; furthermore, various omissions, substitutions and changesin the form of the methods and systems described herein may be madewithout departing from the spirit of the inventions. The accompanyingclaims and their equivalents are intended to cover such forms ormodifications as would fall within the scope and spirit of theinventions.

What is claimed is:
 1. A charged particle beam irradiation method,comprising: dividing a parametric curve that defines a pattern shapeinto a plurality of parametric curves; calculating, for each of theplurality of parametric curves, an area of a region surrounded by asegment connecting end points among control points of the parametriccurve and the parametric curve; calculating positions of vertexes of afigure having an area equivalent to the calculated area and having, asone side thereof, the segment connecting the end points; generating apolygon by using the vertexes; calculating a coverage of the polygon ineach of a plurality of pixels obtained by dividing a target to beirradiated with a charged particle beam into predetermined sizes;calculating an irradiation amount of each of the plurality of pixelsbased on the calculated coverage; and controlling an irradiation unit toirradiate the charged particle beam onto the target with the calculatedirradiation amount.
 2. The method according to claim 1, wherein theparametric curve is a Bezier curve.
 3. The method according to claim 2,wherein the figure is a trapezoid or a triangle having, as a bottom sidethereof, the segment connecting the end points.
 4. The method accordingto claim 2, wherein the Bezier curve is divided at a position of aninflection point.
 5. The method according to claim 1, wherein theparametric curve is divided until a size of a bounding box thatsurrounds a figure having control points of the parametric curve asvertexes thereof becomes equal to or smaller than a predetermined value.6. A charged particle beam irradiation device, comprising: anirradiation unit configured to irradiate a target with a chargedparticle beam; and control circuitry configured to divide a parametriccurve that defines a pattern shape into a plurality of parametriccurves, calculate, for each of the plurality of parametric curves, anarea of a region surrounded by a segment connecting end points amongcontrol points of the parametric curve and the parametric curve,calculate positions of vertexes of a figure having an area equivalent tothe calculated area and having, as one side thereof, the segmentconnecting the end points, generate a polygon by using the vertexes,calculate a coverage of the polygon in each of a plurality of pixelsobtained by dividing a target to be irradiated with the charged particlebeam into predetermined sizes, calculate an irradiation amount of eachof the plurality of pixels based on the calculated coverage, andcontrolling the irradiation unit to emit the calculated irradiationamount.
 7. The charged particle beam irradiation device according toclaim 6, wherein the parametric curve divided by the control circuitryis a Bezier curve.
 8. The charged particle beam irradiation deviceaccording to claim 7, wherein the figure, the vertices of which arecalculated by the control circuitry, is a trapezoid or a trianglehaving, as a bottom side thereof, the segment connecting the end points.9. The charged particle beam irradiation device according to claim 7,wherein the control circuitry is further configured to divide the Beziercurve at a position of an inflection point.
 10. The charged particlebeam irradiation device according to claim 6, wherein the controlcircuitry is further configured to divide the parametric curve until asize of a bounding box that surrounds a figure having control points ofthe parametric curve as vertexes thereof becomes equal to or smallerthan a predetermined value.
 11. A charged particle beam irradiationmethod, comprising: dividing a parametric curve that defines a patternshape into a plurality of parametric curves; generating, for each passof multiple writing of the charged particle beam, a polygon whose shapediffers from one pass to another by using control points that differfrom one pass to another among a plurality of control pointscorresponding to each of the plurality of parametric curves;calculating, for each pass, a coverage of the polygon in each of aplurality of pixels obtained by dividing a target to be irradiated witha charged particle beam into predetermined sizes; calculating anirradiation amount of each of the plurality of pixels based on thecalculated coverage; and controlling an irradiation unit to irradiatethe charged particle beam onto the target with the calculatedirradiation amount.
 12. The method according to claim 11, wherein theparametric curve is a Bezier curve.
 13. The method according to claim12, wherein a first polygon is generated on an outer side of the Beziercurve by drawing segments connecting all control points of the Beziercurve in order; and a second polygon is generated on an inner side ofthe Bezier curve by drawing segments connecting only end points amongthe control points of the Bezier curve in order.
 14. The methodaccording to claim 12, wherein the polygon is generated by using adirection point that differs from one pass to another among theplurality of control points.
 15. The method according to claim 11,wherein the parametric curve is divided until a size of a bounding boxthat surrounds a figure having control points of the parametric curve asvertexes thereof becomes equal to or smaller than a predetermined value.16. A charged particle beam irradiation device, comprising: anirradiation unit configured to irradiate a target with a chargedparticle beam; and control circuitry configured to divide a parametriccurve that defines a pattern shape into a plurality of parametriccurves, generate, for each pass of multiple writing of the chargedparticle beam, the polygon whose shape differs from one pass to anotherby using at least one of a plurality of control points corresponding toeach of the plurality of parametric curves, calculate, for each pass, acoverage of the polygon in each of a plurality of pixels obtained bydividing a target to be irradiated with the charged particle beam intopredetermined sizes, calculate an irradiation amount of each of theplurality of pixels based on the calculated coverage, and control theirradiation unit to emit the calculated irradiation amount.
 17. Thecharged particle beam irradiation device according to claim 16, whereinthe parametric curve divided by the control circuitry is a Bezier curve.18. The charged particle beam irradiation device according to claim 17,wherein the control circuitry is further configured to generate a firstpolygon on an outer side of the Bezier curve by drawing segmentsconnecting all control points of the Bezier curve in order and generatesa second polygon on an inner side of the Bezier curve by drawingsegments connecting only end points among the control points of theBezier curve in order.
 19. The charged particle beam irradiation deviceaccording to claim 17, wherein the control circuitry is furtherconfigured to generate the polygon by using a direction point thatdiffers from one pass to another among the plurality of control points.20. The charged particle beam irradiation device according to claim 16,wherein the control circuitry is further configured to divide theparametric curve until a size of a bounding box that surrounds a figurehaving control points of the parametric curve as vertexes thereofbecomes equal to or smaller than a predetermined value.
 21. Anon-transitory computer-readable recording medium storing a programcausing a computer to execute a process for irradiating a chargedparticle beam onto a target, the process comprising: dividing aparametric curve that defines a pattern shape into a plurality ofparametric curves; calculating, for each of the plurality of parametriccurves, an area of a region surrounded by a segment connecting endpoints among control points of the parametric curve and the parametriccurve; calculating positions of vertexes of a figure having an areaequivalent to the calculated area and having, as one side thereof, thesegment connecting the end points; generating a polygon by using thevertexes; calculating a coverage of the polygon in each of a pluralityof pixels obtained by dividing a target to be irradiated with thecharged particle beam into predetermined sizes; calculating anirradiation amount of each of the plurality of pixels based on thecalculated coverage; and controlling an irradiation unit to irradiatethe charged particle beam onto the target with the calculatedirradiation amount.
 22. A non-transitory computer-readable recordingmedium storing a program causing a computer to execute a process forirradiating a charged particle beam onto a target, the processcomprising: dividing a parametric curve that defines a pattern shapeinto a plurality of parametric curves; generating, for each pass ofmultiple writing of the charged particle beam, a polygon whose shapediffers from one pass to another by using control points that differfrom one pass to another among a plurality of control pointscorresponding to each of the plurality of parametric curves;calculating, for each pass, a coverage of the polygon in each of aplurality of pixels obtained by dividing a target to be irradiated witha charged particle beam into predetermined sizes; calculating anirradiation amount of each of the plurality of pixels based on thecalculated coverage; and controlling an irradiation unit to irradiatethe charged particle beam onto the target with the calculatedirradiation amount.